Two families of nearly optimal codebooks

Chengju Li; Qin Yue; Yiwei Huang

doi:10.1007/s10623-013-9891-7

Two families of nearly optimal codebooks

Chengju Li^*
, Qin Yue
, Yiwei Huang

^*Corresponding author for this work

Nanjing University of Aeronautics and Astronautics
China Pharmaceutical University

Research output: Contribution to journal › Article › peer-review

32 Scopus citations

Abstract

Codebooks are widely applied in code-division multiple-access systems. Recently, several authors constructed codebooks meeting or nearly meeting the Welch bound (i.e. nearly optimal codebooks) using difference set, almost difference set, relative difference set, and so on. In this paper, we will give two families of nearly optimal codebooks. First, we give a class of new almost difference sets and use them to construct nearly optimal codebooks. Second, we present a general construction of codebooks from partial difference sets and obtain several classes of nearly optimal codebooks.

Original language	English
Pages (from-to)	43-57
Number of pages	15
Journal	Designs, Codes, and Cryptography
Volume	75
Issue number	1
DOIs	https://doi.org/10.1007/s10623-013-9891-7
State	Published - Apr 2015
Externally published	Yes

Keywords

Character sums
Difference set
Signal theory

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10.1007/s10623-013-9891-7

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title = "Two families of nearly optimal codebooks",

abstract = "Codebooks are widely applied in code-division multiple-access systems. Recently, several authors constructed codebooks meeting or nearly meeting the Welch bound (i.e. nearly optimal codebooks) using difference set, almost difference set, relative difference set, and so on. In this paper, we will give two families of nearly optimal codebooks. First, we give a class of new almost difference sets and use them to construct nearly optimal codebooks. Second, we present a general construction of codebooks from partial difference sets and obtain several classes of nearly optimal codebooks.",

keywords = "Character sums, Difference set, Signal theory",

author = "Chengju Li and Qin Yue and Yiwei Huang",

note = "Publisher Copyright: {\textcopyright} 2013, Springer Science+Business Media New York.",

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AB - Codebooks are widely applied in code-division multiple-access systems. Recently, several authors constructed codebooks meeting or nearly meeting the Welch bound (i.e. nearly optimal codebooks) using difference set, almost difference set, relative difference set, and so on. In this paper, we will give two families of nearly optimal codebooks. First, we give a class of new almost difference sets and use them to construct nearly optimal codebooks. Second, we present a general construction of codebooks from partial difference sets and obtain several classes of nearly optimal codebooks.

KW - Character sums

KW - Difference set

KW - Signal theory

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Two families of nearly optimal codebooks

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Keywords

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